Related papers: Cohomological descent on the overconvergent site

We give applications of the higher Lefschetz theorems for foliations of [BH10], primarily involving Haefliger cohomology. These results show that the transverse structures of foliations carry important topological and geometric information.…

Let $X^n$ be a nonsingular hypersurface of degree $d\geq 2$ in the projective space $\mathbb{P}^{n+1}$ defined over a finite field $\mathbb{F}_q$ of $q$ elements. We prove a Homma-Kim conjecture on a upper bound about the number of…

We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for vector bundles.

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of…

We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…

We develop the (co)homological tools that make effective the construction of the quaternionic Darmon points introduced by Matthew Greenberg. In addition, we use the overconvergent cohomology techniques of Pollack--Pollack to allow for the…

In this paper, we show that an irreducible proper complex equifocal submanifold of codimension greater than one in a symmetric space of non-compact type. The proof is performed by showing the homogeneity of the lift of the complexification…

We prove that for any discrete group $G$ with finite $\mathfrak{F}$-cohomological dimension, the Gorenstein cohomological dimension equals the $\mathfrak{F}$-cohomological dimension. This is achieved by constructing a long exact sequence of…

We prove a selection theorem for paraconvex-valued mappings defined on {\tau}-PF normal spaces. The method developed to prove this result is used to provide a general approach to such selection theorems.

Hrushovski's generalization and application of [Jouanolou, "Hypersurfaces solutions d'une \'equation de Pfaff analytique", Mathematische Annalen, 232 (3):239--245, 1978] is here refined and extended to the partial differential setting with…

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW-complexes equipped with the action of a group of prime order $p$ whose $p$-torsion cohomology can be killed by…

The (Fg) condition on Hochschild cohomology as well as the support variety theory are shown to be invariant under derived equivalence.

We consider the crystalline realization of Deligne's 1-motives in positive characteristics and prove a comparison theorem with the De Rham realization of liftings to zero characteristic. We then show that one dimensional crystalline…

We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We study cohomology for $p$-local finite groups with non-constant coefficient systems. In particular we show that under certain restrictions there exists a cohomology transfer map in this context, and deduce the standard consequences.

We define and provide some basic analysis of various types of crossed products by semimultiplicative sets, and then prove a $KK$-theoretical descent homomorphisms for semimultiplicative sets in accord with the descent homomorphism for…

It is proved that for any Grothendieck site $X$, there exists a coreflection (called $\mathbf{cosheafification}$) from the category of precosheaves on $X$ with values in a category $\mathbf{K}$, to the full subcategory of cosheaves,…

We review the recent progress in the study of cyclic cohomology in the presence of Hopf symmetry.

Hayman's conjecture about covering of vertical intervals under regular mappings is proved.